The etymology of spud is that this name for a small potato comes from the digging of soil (or a hole) prior to the planting of potatoes. The word is of unknown origin and was originally (c. 1440) used as a term for a short knife or dagger, probably related to Dutch spyd. The word spud traces back to the 16th century. It subsequently transferred over to a variety of digging tools. Around 1845 it transferred over to the tuber itself.
The origins of "spud" has erroneously been attributed to a 19th century activist group dedicated to keeping the potato out of Britain, calling itself The Society for the Prevention of an Unwholesome Diet.
It was Mario Pei's 1949 The Story of Language that can be blamed for the false origin of the word. Pei writes, "the potato, for its part, was in disrepute some centuries ago. Some Englishmen who did not fancy potatoes formed a Society for the Prevention of Unwholesome Diet. The initials of the main words in this title gave rise to spud." Like many other pre-20th century acronymic origins, this one is false.